At some level you could say that the U.S. measurements are "based on metric" since almost all of them are defined in terms of metric units. You just have to apply the proper factor (which is a decimal, but a terminating one --- unlike the sqrt(2) business).
Also, the word "metric" has a very precise meaning: that of being part of the internationally agreed system of decimal measurements. The thing you've mentioned don't fit that definition, and US customary units are simply defined in _terms_ of metric units, but are not metric units themselves.
I do understand it. It's exactly the same reasoning as being able to divide liquid measures in half.
> By that standard, the U.S. liquid measures could also be described as "metric"
The ratio has nothing to do with metric. The base sizing of the A0 page is, on the other hand, defined as having an area of 1m² in that regard, DIN/ISO paper sizes are _based_ on metric. However, _never_ did I state that they _were_ metric.
So no, by the standard that I gave, you _couldn't_ say that US customary measurements for liquid measures could also be described as "metric".
Go back and read my original comment. The first sentence was this:
> They're not part of the metric system, simply based on it.
Here I was making reference to A0 sheets being defined as having an area of 1m², thus the sheet sizes are _derived_ from metric, not _part_ of the metric system.
The next sentence was a _completely_ independent statement about the utility of the page ratio used in ISO/DIN paper sizes:
> The 1:sqrt(2) ratio used is extremely convenient as it scales up and down nicely, and the other series are such that an Ax sheet fits nicely into a Cx envelope, and a Cx sheet fits nicely into a Bx envelope.
I can't fathom how you somehow got from an innocuous pair of statements about paper sizes to powers of two in US customary measurements for liquids somehow being "metric".
The official definition of the inch is 2.54 cm (exactly).
An inch isn't a nice round number of cm, but neither is an A(whatever) piece of paper (other than A0). A4 is 21.0 cm × 29.7 cm. for instance.
"The next sentence was a _completely_ independent statement about the utility of the page ratio used in ISO/DIN paper sizes"
And I pointed out that the exact same argument applies to U.S. liquid measures. They're easy to divide or multiply by two.
Your comparison to liquid measurements misses the point. It's irrelevant. Your statement that the US units are defined in terms of US units is irrelevant.
What is relevant is the preservation of the width:height ratio between pages sizes in the ISO/DIN paper size series.
Which is very similar to the "magic property" that you get when you have measuring units that are powers of two rather than factors of ten. So, no, I"m not "missing the point" at all.
That you think this is "irrelevant" indicates to me that you haven't done a lot of cooking.
The 1:sqrt(2) ratio has to do with subdivision. An A0 sheet subdivides into two A1 sheets, which subdivides into two A2 sheets, and so on. 1:sqrt(2) width/height ratio used in ISO pages sizes allows this, which makes dealing with paper significantly easier when it comes to slicing up pages, folding, packing, &c.